BERLIN — German Chancellor Angela Merkel on Tuesday reassured Ireland that it can rely on Germany in Brexit talks as the European Union and Britain struggle to find a way to maintain an open Irish border after the UK leaves.

Merkel met with Irish Prime Minister Leo Varadkar in Berlin a day after EU and British negotiators said there had been no breakthrough on the Irish border issue, despite announcing progress on the outlines of a transition deal.

‘‘A solution must be found for this . . . and Germany fully supports the Irish position,’’ Merkel said.

Britain is due to leave the 28-nation European Union in a little over a year, and how to keep open the border between EU member state Ireland and Northern Ireland, which is part of the United Kingdom, is proving to be difficult.

Varadkar stressed that a ‘‘backstop solution’’ under which Northern Ireland would remain part of the EU’s tariff-free customs union while the rest of the United Kingdom leaves must ‘‘apply unless and until a workable alternative agreed solution is found.’’

ASSOCIATED PRESS